Question

Kindly refer to the following figure and please help me find angle HGB AND FHD. THE ANGLES ARE MARKED 

Answer 1

If lines BG and DH are parallel, angle BGH = (3 x - 10)     { is it -10 or + 10 ???
                                             angle FHD = (5 x - 11)

The lines BG & DH are parallel then, sum of included angles is 180 deg.
Angles  ( 5 x - 11 ) + ( 3 x - 10)  = 180 deg
  So,    8 x - 21 = 180      x = 201 /11

Angle HGB = 3 *201/11 - 10 deg

Angle FHD = 5 *201/11 - 11 deg

Answer 2

Angle HGB = 180 - (5x - 11) and 

FHD = 180 - (3x + 10)

But angle G and H sum up to 180 degrees as they lie on the same side of the transversal line (assumed to horizontal lines as parallel)

Therefore, 5x - 11 + 3x + 10 = 180
⇒ 8x = 181
⇒ x =  22.625
Now,
Angle HGB = 180 - (5(22.625) - 11) = 180 - 113.125 + 11 = 77.875

and 

FHD = 180 - (3(22.625) + 10) = 180 - 67.875 - 10 = 102.125